posfloor

the question

Does Based's second-order Taylor attention weight have an exact positivity floor, and what selectivity cost does that floor impose relative to softmax?

what came out

The weight 1+t+t^2/2 has minimum exactly 1/2, so a key can never fall below half its unnormalized weight where softmax goes to zero. Order two is the minimal positive Taylor truncation with the largest floor. Singling out one key against N needs alignment growing like sqrt(N) versus softmax's log(N), a gap widening to 13x at N=16384.

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